A logistic approximation to the cumulative normal distribution
A logistic approximation to the cumulative normal distribution
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DOI：
10.3926/jiem.2009.v2n1.p114-127
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发表时间：
2009-01-01
影响因子：
3
通讯作者：
Cho, Byung Rae
中科院分区：
文献类型：
--
作者：
Bowling, Shannon R.;Khasawneh, Mohammad T.;Cho, Byung Rae
本文提出了一种累积正态分布的Logistic近似。虽然文献中包含了大量的正态分布的近似函数，但它们非常复杂，不是很准确，或者只在有限的范围内有效。本文提出了一种改进的近似函数。当将所提出的函数与文献中研究的其他近似进行比较时，可以观察到所提出的逻辑近似具有更简单的函数形式，并且它提供了更高的精度，对于整个范围，最大误差小于0.00014。据作者所知，这是文献中报告的最低水平的错误。建议的逻辑近似函数可能会吸引研究人员，从业者和教育工作者，因为它的功能简单和数学精度。
This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors' knowledge, the lowest level of error reported in the literature. The proposed logistic approximate function may be appealing to researchers, practitioners and educators given its functional simplicity and mathematical accuracy.